Algorithm 2.

AdaBoost with Reject Option Algorithm

Given: -(x1, y1), …, (xm, ym) where xi ∈ χ, y ∈ {−1, +1} -ε : false negative rate upper bound -λ : indecision weight -τ : stopping condition threshold -T : maximum allowed number of rounds
1:	procedure Train(data)
2:	Initialize example i weight at iteration 1: D1(i) = 1/m for i = 1, …, m
3:	for t=1,…,T do
4:	Train weak classifier using distribution Dt
5:	Find weak learner at iteration t: ht, ${\beta }_t=\text{arg }\underset{h_j\in H,{\beta }_t}{\text{min}}⧣\text{FP}+\lambda \ast ⧣\text{IND}$ $$\text{subject to}\mathit{\text{FNR}}=\frac{\mathit{\text{FN}}}{\mathit{\text{TP}}+\mathit{\text{FN}}}\le \epsilon$$
6:	Choose weak learner weight ${\alpha }_t=\frac{1}{2}\text{ln}(\frac{1-{\epsilon }_t}{{\epsilon }_t})$
7:	Update $D_{t+1}(i)=\frac{D_t(i)\text{exp}(-{\alpha }_t{y}_i{h}_t(x_i))}{Z_t}$ where Zt is normalization factor
8:	If δFPR| ≤ 0 and δINDR ≥ τ then break
9:	Return final classifier: H(x)